Lagrangian Manifolds and Efficient Short-Wave Asymptotics in a Neighborhood of a Caustic Cusp

被引:0
作者
S. Yu. Dobrokhotov
V. E. Nazaikinskii
机构
[1] Ishlinsky Institute for Problems in Mechanics,
[2] Russian Academy of Sciences,undefined
来源
Mathematical Notes | 2020年 / 108卷
关键词
semiclassical asymptotics; canonical operator; caustic; cusp; Pearcey function; efficient formula;
D O I
暂无
中图分类号
学科分类号
摘要
引用
收藏
页码:318 / 338
页数:20
相关论文
共 49 条
[1]  
Dobrokhotov S. Yu.(2017)New integral representations of the Maslov canonical operator in singular charts Izv. Math. 81 286-328
[2]  
Nazaikinskii V. E.(1946)The structure of an electromagnetic field in the neighbourhood of a cusp of a caustic Philos. Mag. (7) 37 311-317
[3]  
Shafarevich A. I.(1957)An extension of the method of steepest descents Proc. Cambridge Philos. Soc. 53 599-611
[4]  
Pearcey T.(1962)Geometrical theory of diffraction J. Opt. Soc. Amer. 52 116-130
[5]  
Chester C.(1966)Uniform asymptotic expansions at a caustic Comm. Pure Appl. Math. 19 215-250
[6]  
Friedman B.(1967)Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities J. Math. Mech. 17 533-559
[7]  
Ursell F.(1972)Integrals with a large parameter. Several nearly coincident saddle points Proc. Cambridge Philos. Soc. 72 49-65
[8]  
Keller J. B.(1974)Oscillatory integrals, Lagrange immersions and unfolding of singularities Comm. Pure Appl. Math. 27 207-281
[9]  
Ludwig D.(1980)Phase-space projection identities for diffraction catastrophes J. Phys. A 13 149-160
[10]  
Bleistein N.(1981)Theory of cusped rainbows in elastic scattering: uniform semiclassical calculations using Pearcey’s integral J. Chem. Phys. 75 2831-2846